This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(4)=13 since 13 is the fourth prime in A068947.
A007953 := proc(n) option remember: return add(d, d=convert(n, base, 10)): end: A068947 := proc(n) option remember: local k, p: if(n=1)then return 1: fi: k:=procname(n-1): p:=A007953(k^2): do k:=k+1: if(A007953(k^2)>p)then return k: fi: od: end: seq(A068947(n)^2, n=1..20); # Nathaniel Johnston, May 04 2011
t = {}; s = 0; Do[If[(x = Total[IntegerDigits[y = n^2]]) > s, AppendTo[t, y]; s = x], {n, 150000}]; t (* Jayanta Basu, Aug 06 2013 *)
The respective digit averages are: n | a(n) | a(n)^2 | #digits | sum(digits) | digit average ----+-----------+------------------+---------+-------------+------------------ - | 4 | 16 | 2 | 7 | 7/2 = 3.5 - | 6 | 36 | 2 | 9 | 9/2 = 4.5 - | 7 | 49 | 2 | 13 | 13/2 = 6.5 0 | 10 | 100 | 3 | 1 | 1/3 = 0.333... 1 | 11 | 121 | 3 | 4 | 4/3 = 1.333... 2 | 12 | 144 | 3 | 9 | 3 = 3.0 3 | 13 | 169 | 3 | 16 | 16/3 = 3.333... 4 | 17 | 289 | 3 | 19 | 19/3 = 6.333... 5 | 63 | 3969 | 4 | 27 | 27/4 = 6.75 6 | 83 | 6889 | 4 | 31 | 31/4 = 7.75 7 | 313 | 97969 | 5 | 40 | 8 = 8.0 8 | 94863 | 8998988769 | 10 | 81 | 81/10 = 8.1 9 | 3162083 | 9998768898889 | 13 | 106 | 106/13 = 8.15... 10 | 994927133 |989879999979599689| 18 | 148 | 74/9 = 8.222...
m=0; for(k=10,oo, vecsum(d=digits(k^2))>m*#d && !print1(k", ") && m=vecsum(d)/#d)
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